cp's OEIS Frontend

A353780 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1), does not equal a(n-1)+1, and has no digit in common with a(n-1).

%I A353780 #11 May 23 2022 17:46:12
%S A353780 1,3,2,5,4,7,6,11,8,13,9,14,23,10,27,16,25,17,20,19,22,15,26,31,24,35,
%T A353780 12,37,18,29,33,28,39,41,30,47,21,34,55,32,45,38,49,36,59,40,51,43,50,
%U A353780 61,42,53,44,57,46,71,48,65,72,83,52,63,58,67,54,73,56,79,60,77,62,75,64,81,70
%N A353780 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1), does not equal a(n-1)+1, and has no digit in common with a(n-1).
%C A353780 The sequence is conjectured to be a permutation of the positive integers.
%H A353780 Scott R. Shannon, <a href="/A353780/a353780.png">Image of the first 75000 terms</a>. The green line is y = n.
%e A353780 a(15) = 27 as a(14) = 10, and 27 has not yet appeared, is coprime to 10, is not 1 more than 10, and has no digit in common with 10. Note that 21 satisfies all of these conditions except the last. This is the first term to differ from A353904.
%o A353780 (Python)
%o A353780 from math import gcd
%o A353780 from itertools import islice
%o A353780 def c(san, k): return set(san) & set(str(k)) == set()
%o A353780 def agen(): # generator of terms
%o A353780     an, aset, mink = 1, {1}, 2
%o A353780     while True:
%o A353780         yield an
%o A353780         k, san = mink, str(an)
%o A353780         while k in aset or gcd(an, k) != 1 or k-an == 1 or not c(san, k):
%o A353780             k += 1
%o A353780         an = k
%o A353780         aset.add(an)
%o A353780         while mink in aset: mink += 1
%o A353780 print(list(islice(agen(), 75))) # _Michael S. Branicky_, May 23 2022
%Y A353780 Cf. A353904, A093714, A068861, A109812.
%K A353780 nonn,base
%O A353780 1,2
%A A353780 _Scott R. Shannon_, May 07 2022